## RE: [APBR_analysis] Re: Defensing the Mavs

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• ... From: igorkupfer@rogers.com [mailto:igorkupfer@rogers.com] Sent: Thursday, May 22, 2003 6:44 PM ... From: harlanzo To:
Message 1 of 11 , May 24, 2003
-----Original Message-----
From: igorkupfer@... [mailto:igorkupfer@...]
Sent: Thursday, May 22, 2003 6:44 PM

----- Original Message -----
From: harlanzo
Sent: Thursday, May 22, 2003 9:17 PM
Subject: [APBR_analysis] Re: Defensing the Mavs

The other thing with bowen is sample size.  he is a bad free throw
shooter but he rarely goes to line (1.1 per game).  In the two years
that bowen shot over 100 free throws he shot about 61%.  I suspect
the more you foul him the less it helps.
I don't think so -- there doesn't seem to be much of a pattern when you look at his FT% broken down by FTA in each game:

FTA    games    FT%
1      16     37.5%
2     105     52.4%
3      11     48.5%
4      42     57.1%
5       5     64.0%
6       9     53.7%
7       3     47.6%
8       3     66.7%
9       1     66.7%

ed

[Michael Tamada]   Actually those numbers do indicate a weak positive relationship between Bowen's FTA and FT%.  If we simply regress the FT% on the FTA (so, just 9 observations), a linear regression suggests that his FT% rises by 2.6 percentage points for each additional  FTA he attempts.  This is significant at the p=2.9% level (adjusted R2 = .45).

That simple 9-observation regression of course is misleading because some of those FTA/FT% combinations occured a lot more frequently than others.  When we treat each game as an observation (so 195 observations), we get a worse fit (adjusted R2 = .39), and a smaller slope estimate (2.3 percentage point increase in FT%), but with the larger number of observations the results become highly statistically significant (p < 1%).

Pretty much the same results can be obtained by using a simpler technique:  really, the only combinations with large numbers of observations are 2 FTA and 4 FTA.  Bowen's FT% appears to rise from 52.4% to 57.1% over that range, implying that each FTA raises his FT% by 2.35 percentage points.

If we take the regression equation literally, then each additional FTA per game raises Bowen's FT% by 2.3 percentage points -- implying that the marginal FTA has a 4.6 high percentage point probability than the previous one.  And given his estimate y-intercept of .460,  if  Bowen ever attempts 11 FTs in a game, he'll have over a 100% probability of making his 12th FT!  ;)

--MKT

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